Does ferroelectric quantum criticality raise the $T_{c}$ of SrTiO3
In plain words
SrTiO3 is close to becoming ferroelectric, meaning its ions almost shift to create a permanent electric dipole. Pushing it closer, by replacing oxygen-16 with oxygen-18 or adding calcium, raises its superconducting temperature, and the reason is debated.
Precise statement
18O substitution, Ca substitution and strain move n-doped SrTiO3 toward its ferroelectric quantum critical point and raise $T_c$, in some reports by about a factor of 2. Determine whether the enhancement is caused by pairing through the critical soft transverse-optical mode, which electron-phonon coupling is responsible (linear Rashba-type or bilinear two-phonon), and where $T_c$ peaks relative to the critical point (paraelectric side, at criticality, or inside the polar phase). An answer is a mechanism with a quantitative fit of $T_c$ versus distance to criticality and carrier density.
What would settle it
Measurement of $T_{c}$ across the ferroelectric critical point at fixed n under continuous tuning (stress or isotope fraction) compared with a soft-mode pairing calculation with no free couplings.